Question: Simplify the following expression: $ n = \dfrac{-1}{7} - \dfrac{-10}{8y - 7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8y - 7}{8y - 7}$ $ \dfrac{-1}{7} \times \dfrac{8y - 7}{8y - 7} = \dfrac{-8y + 7}{56y - 49} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-10}{8y - 7} \times \dfrac{7}{7} = \dfrac{-70}{56y - 49} $ Therefore $ n = \dfrac{-8y + 7}{56y - 49} - \dfrac{-70}{56y - 49} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-8y + 7 + 70 }{56y - 49} $ Distribute the negative sign: $n = \dfrac{-8y + 7 + 70}{56y - 49}$ $n = \dfrac{-8y + 77}{56y - 49}$